Transmission power allocation of NCSs with Markov channel assignment

Abstract

This paper investigates networked control systems (NCSs) where the sensors communicate with the remote controller via a wireless fading channel. Each time the channel can accommodate just one sensor for communication and the access to the channel of the sensors is driven by a random event. When a sensor is triggered to send its measurement, it can choose to use a high power or a low power to save energy. The power level of the sensor determines the probability of successful packet reception at the controller. This paper aims to find an appropriate transmission power allocation method for the sensors jointly with a system controller so that the NCS is stabilized with a given energy budget. By introducing a Markov chain model for the medium-access constraint and modeling the packet dropout as a Bernoulli process, we derive a new model and stability conditions for the NCSs, which are given in terms of the transition probabilities of the Markov chain and different packet reception rates. An interesting power scheduling policy is obtained and two kinds of controller design schemes are given depending on whether the medium-access status of the sensors is acknowledged to the controller or not. The results are then extended to the case of large-scale systems and an optimal co-design methodology which can stabilize the whole set of systems with largest stability margin is proposed. The effectiveness of the presented method is demonstrated by numerical simulations.